Książki: „GEP EQUATION”

1

Gesztesy, Fritz. (m)KdV solitons on the background of quasi-periodic finite-gap solutions. Providence, R.I: American Mathematical Society, 1995.

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Simos, Th. Forecasting quarterly GDP using a system of stochastic differential equations. Athens: Centre of Planning and Economic Research, 2002.

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Dyall, Kenneth G. All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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Dyall, Kenneth G. All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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5

Master math: Solving word problems : analyze any word problem, translate it into mathematical terms, and get the right answer! Boston, MA: Course Technology, 2010.

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1942-, Bulla W., red. Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies. Providence, R.I: American Mathematical Society, 1998.

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Martin, Gutting, i SpringerLink (Online service), red. Special Functions of Mathematical (Geo-)Physics. Basel: Springer Basel, 2013.

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la, Llave Rafael de, i Seara Tere M. 1961-, red. A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Heuristics and rigorous verification on a model. Providence, R.I: American Mathematical Society, 2006.

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9

Center, Langley Research, red. Expanded equations for torque and force on a cylindrical permanent magnet core in a large-gap magnetic suspension system. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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Groom, Nelson J. Expanded equations for torque and force on a cyclindrical permanent magnet core in a large-gap magnetic suspension system. Washington, D.C: National Aeronautics and Space Administration, 1997.

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11

Rajeev, S. G. Geometric Integrators. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0015.

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Generic methods for solving ordinary differential equations (ODEs, e.g., Runge-Kutta) can break the symmetries that a particular equation might have. Lie theory can be used to get Geometric Integrators that respect these symmetries. Extending thesemethods to Euler and Navier-Stokes is an outstanding research problem in fluid mechanics. Therefore, a short review of geometric integrators for ODEs is given in this last chapter. Exponential coordinates on a Lie group are explained; the formula for differentiating a matrix exponential is given and used to derive the first few terms of the Magnus expansion. Geometric integrators corresponding to the Euler and trapezoidal methods for ODEs are given.

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12

Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

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Fratianni, Michele. The Gravity Equation in International Trade. Redaktor Alan M. Rugman. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780199234257.003.0003.

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This article aims to explain trade flows in terms of the gravity equation (GE). The reason for focusing on GE is twofold. The first is that GE, unlike other frameworks, has had great empirical success in explaining bilateral trade flows. For a long time, however, GE was a child without a father in the sense that it was thought to have no theoretical support. Since the late 1970s, this state of affairs has changed radically. Now, the gravity equation has strong theoretical support and can be derived from a variety of models of international trade. The second is that GE can be used to sort out alternative hypotheses of international trade.

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14

Atangana, Abdon. Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology. Elsevier Science & Technology Books, 2017.

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Atangana, Abdon. Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology. Elsevier Science & Technology Books, 2017.

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16

Haq, Khadija, red. Development, Employment, and Income Distribution. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199474684.003.0009.

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In the chapter, Haq raises questions about the spurious relationship between GNP growth, employment and income distribution. Two decades of development experience of many developing countries suggested that high GNP growth did not guarantee elimination of unemployment or poverty reduction. He cites examples of development policies of India, Pakistan and Brazil to illustrate their preoccupation with GNP growth and their assumption that income distribution policies could be divorced from growth policies and could be added later to the equation. In this paper, Haq redefines the problem of development from GNP growth to a ‘selective attack on the worst form of poverty’. He also stresses on the need to treating employment as the primary objective of planning and using development and income redistribution policies in tandem, rather than thinking about redistribution after growth has materialized.

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17

Morawetz, Klaus. Systems with Condensates and Pairing. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0012.

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The Bose–Einstein condensation and appearance of superfluidity and superconductivity are introduced from basic phenomena. A systematic theory based on the asymmetric expansion of chapter 11 is shown to correct the T-matrix from unphysical multiple-scattering events. The resulting generalised Soven scheme provides the Beliaev equations for Boson’s and the Nambu–Gorkov equations for fermions without the usage of anomalous and non-conserving propagators. This systematic theory allows calculating the fluctuations above and below the critical parameters. Gap equations and Bogoliubov–DeGennes equations are derived from this theory. Interacting Bose systems with finite temperatures are discussed with successively better approximations ranging from Bogoliubov and Popov up to corrected T-matrices. For superconductivity, the asymmetric theory leading to the corrected T-matrix allows for establishing the stability of the condensate and decides correctly about the pair-breaking mechanisms in contrast to conventional approaches. The relation between the correlated density from nonlocal kinetic theory and the density of Cooper pairs is shown.

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18

Schwarz, Eric. Opportunity Equation: How Citizen Teachers Are Combating the Achievement Gap in America's Schools. Beacon Press, 2014.

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19

All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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20

Sandor, Jozsef. Geometric Theorems, Diophantine Equations, and Arithmetic Functions. American Research Press, 2002.

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21

The opportunity equation: How citizen teachers are combating the achievement gap in America's schools. Beacon Press, 2014.

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22

Cosculluela, Cécile. English Verb Equation: An Easy Six-Step Logic to Get Your Verb Forms Right. Independently Published, 2022.

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Cosculluela, Cécile. English Verb Equation: An Easy Six-Step Logic to Get Your Verb Forms Right. Independently Published, 2022.

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24

Practical Guide to Geo-Engineering: With Equations, Tables, Graphs and Check Lists. Springer Netherlands, 2014.

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25

Williams, Kenneth R. Crowning Gem: One Vedic Master-Formula for Powers, Roots and Polynomial Equations. Learning Analytic Pte. Ltd., 2015.

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Srbulov, Milutin. Practical Guide to Geo-Engineering: With Equations, Tables, Graphs and Check Lists. Springer London, Limited, 2014.

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Srbulov, Milutin. Practical Guide to Geo-Engineering: With Equations, Tables, Graphs and Check Lists. Springer, 2016.

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28

Solymar, L., D. Walsh i R. R. A. Syms. Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198829942.003.0014.

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The Meissner effect is discussed. The latent heat of transition is derived by a thermodynamic approach. The concept of surface energy is introduced, leading to the distinction between Type I and Type II superconductors. The differential equation for the superconducting wave function is derived. The energy gap and the phenomenon of tunnelling are discussed. The difference between superconducting tunnelling and Josephson tunnelling is explained. The significance of high transition temperature superconductors is discussed. It is shown that an important application of superconductors is to produce high-field magnets.

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29

The Empowered Mind Diet Equation: Get To The Best Version Of Yourself Via Diet & Mind. Tellwell Talent, 2018.

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The Talent Equation Big Data Lessons For Navigating The Skills Gap And Building A Competitive Workforce. McGraw-Hill Education - Europe, 2013.

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31

WeSolveThem. Algebra Equations: Everything a Student Needs to Get Through an Algebra Course in College! Independently Published, 2017.

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32

Rajeev, S. G. Shocks. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0006.

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When the speed of a fluid exceeds that of sound, discontinuities in density occur, called shocks.The opposite limit from incompressibility (constant density) is constant pressure. In this limit, we get Burgers equation. It can be solved exactly in one dimension using the Cole–Hopf transformation. The limit of small viscosity is found not to be the same as zero viscosity: there is a residual drag no matter how small it is. The Maxwell construction of thermodynamics was adapted by Lax and Oleneik to derive rules for shocks in this limit. The Riemann problem of time evolution with a discontinuous initial density is solved in one dimension. These simple solutions provide the basic intuition for more complicated shocks.

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33

Price, David. How to get an A in-- senior algebra: Non-linear equations, exponential functions, logarithmic functions. Coles, 2001.

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34

Getting The People Equation Right How To Get The Right People In The Right Jobs And Keep Them. Logan Loomis, LLC, 2011.

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35

Nelder, John A., Yudi Pawitan i Youngjo Lee. Generalized Linear Models with Random Effects: Unified Analysis Via H-Likelihood, Second Edition. Taylor & Francis Group, 2017.

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36

Nelder, John A., Yudi Pawitan i Youngjo Lee. Generalized Linear Models with Random Effects: Unified Analysis Via H-Likelihood. Taylor & Francis Group, 2006.

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37

Allen, Michael P., i Dominic J. Tildesley. Mesoscale methods. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803195.003.0012.

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Coarse-graining is an increasingly commonplace approach to study, as economically as possible, large-scale, and long-time phenomena. This chapter covers the main methods. Brownian and Langevin dynamics are introduced, with practical details of the solution of the modified equations of motion. Several techniques which aim to bridge the gap to the hydrodynamic regime are described: these include dissipative particle dynamics, multiparticle collision dynamics, and the lattice Boltzmann method. Several examples of program code are provided. In the last part of the chapter, the derivation of a coarse-grained potential from an atomistic one is considered using force-matching and structure-matching, and the limitations of these approaches are discussed.

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Ltd, ICON Group, i ICON Group International Inc. EQUATOR GROUP PLC: International Competitive Benchmarks and Financial Gap Analysis (Financial Performance Series). Wyd. 2. Icon Group International, 2000.

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Chruściel, Piotr T. Geometry of Black Holes. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198855415.001.0001.

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There exists a large scientific literature on black holes, including many excellent textbooks of various levels of difficulty. However, most of these prefer physical intuition to mathematical rigour. The object of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject. The first part of the book starts with a presentation, in Chapter 1, of some basic facts about Lorentzian manifolds. Chapter 2 develops those elements of Lorentzian causality theory which are key to the understanding of black-hole spacetimes. We present some applications of the causality theory in Chapter 3, as relevant for the study of black holes. Chapter 4, which opens the second part of the book, constitutes an introduction to the theory of black holes, including a review of experimental evidence, a presentation of the basic notions, and a study of the flagship black holes: the Schwarzschild, Reissner–Nordström, Kerr, and Majumdar–Papapetrou solutions of the Einstein, or Einstein–Maxwell, equations. Chapter 5 presents some further important solutions: the Kerr–Newman–(anti-)de Sitter black holes, the Emperan–Reall black rings, the Kaluza–Klein solutions of Rasheed, and the Birmingham family of metrics. Chapters 6 and 7 present the construction of conformal and projective diagrams, which play a key role in understanding the global structure of spacetimes obtained by piecing together metrics which, initially, are expressed in local coordinates. Chapter 8 presents an overview of known dynamical black-hole solutions of the vacuum Einstein equations.

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40

Ready, Jonathan L. Shared Similes in the Homeric Epics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198802556.003.0006.

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Our Homeric poets strove to display their competence by doing what their predecessors and peers did. To discover the shared similes in the Iliad and the Odyssey, the chapter first reviews the (nearly) verbatim short vehicle portions and similar long vehicle portions found (a) in the Iliad and Odyssey or (b) in the Iliad or Odyssey and in other archaic Greek hexameter poems or lyric poems. The chapter then discusses “scenarios” to get at the mental templates underlying many of our Homeric poets’ vehicle portions, templates that reveal the extent of their use of shared vehicle portions. By linking this model of scenarios with an approach from cognitive linguistics known as Frame Semantics, one can detect the ease with which a Homeric poet learned the scenarios. Our poets’ demonstrations of their use of shared elements also comes to the fore when one examines their similes as two-part equations, each composed of a tenor and a vehicle.

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41

Draganov, Alexandr. Mathematical Tools for Real-World Applications. The MIT Press, 2022. http://dx.doi.org/10.7551/mitpress/14218.001.0001.

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Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found in textbooks: they are messier, take longer to solve, and standard solution recipes might not apply. This book fills the gap between what is taught in the typical college curriculum and what a practicing engineer or scientist needs to know. It presents six powerful tools for analysis, research, and problem solving in the real world: dimensional analysis, limiting cases, symmetry, scaling, making order of magnitude estimates, and the method of successive approximations. The book does not focus on formulaic manipulations of equations, but emphasizes analysis and explores connections between the equations and the application. Each chapter introduces a set of ideas and techniques and then shows how these techniques apply to a series of problems. (Knowledge of algebra and trigonometry, but not calculus, is required.) The final two chapters tie all six techniques together and apply them to two real-world problems: computing the probability of a rare, catastrophic event, and tracking a satellite with a GPS receiver. Readers will learn how to analyze, dissect, and gain insight into the results by using all the techniques presented in earlier chapters—and discover how analysis tools work on problems not concocted for a textbook. The appendix provides solutions to many of the problems found throughout the book. Alexandr Draganov was born and raised in Kyiv, Ukraine; in light of the current war in Ukraine he will donate 100% of his royalties for the first year to support medical and humanitarian efforts there.

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42

Heinrich, Joel G. A comparison of the (chemical equation) Drell-Yan cross section at 80 and 250 GEV/C and a measurement of the proton structure function sea/valence ratio. 1988.

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43

Publish, Direct. Algebra Quadratic Equation Workbook Practice and Compare with the Solution: Practice This Problems and You Will Get Your Algebra Skills and Knowledge Improved. Note Pages for Practice Inside. Independently Published, 2020.

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44

Nelder, John A., Yudi Pawitan i Youngjo Lee. Generalized Linear Models with Random Effects: Unified Analysis Via H-Likelihood, Second Edition. Taylor & Francis Group, 2018.

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Generalized Linear Models with Random Effects: Unified Analysis Via H-Likelihood, Second Edition. Taylor & Francis Group, 2018.

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46

Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood (Monographs on Statistics and Applied Probability). Chapman & Hall/CRC, 2006.

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Nelder, John A., Yudi Pawitan i Youngjo Lee. Generalized Linear Models with Random Effects: Unified Analysis Via H-Likelihood, Second Edition. Taylor & Francis Group, 2018.

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Nelder, John A., Yudi Pawitan i Youngjo Lee. Generalized Linear Models with Random Effects. Taylor & Francis Group, 2021.

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Nelder, John A., Yudi Pawitan i Youngjo Lee. Generalized Linear Models with Random Effects: Unified Analysis Via H-Likelihood. Taylor & Francis Group, 2010.

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50

Nelder, John A., Yudi Pawitan i Youngjo Lee. Generalized Linear Models with Random Effects: Unified Analysis Via H-Likelihood, Second Edition. Taylor & Francis Group, 2018.

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